.. _getri_batch-group-version:

getri_batch (Group Version)
===========================


Computes the batch of inverses of an LU-factored general matrices
determined by the ``getrf_batch`` (Group Version) function. This routine
belongs to the ``oneapi::mkl::lapack`` namespace.


.. contents::
    :local:
    :depth: 1

Description
***********

The routine computes the inverses ``A``\ :sub:`1`\ :sup:`-1` of a
general matrices ``A``\ :sub:`1`, ``iϵ{1...batch_size}``. Before
calling this routine, call :ref:`getrf_batch-group-version` function
to factorize ``A``\ :sub:`1`.


The total number of problems to solve, ``batch_size``, is a sum of sizes
of all of the groups of parameters as provided by
``group_sizes``\ array.


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::lapack {
     cl::sycl::event getri_batch(cl::sycl::queue &queue,
     std::int64_t *n,
     T **a,
     std::int64_t *lda,
     std::int64_t **ipiv,
     std::int64_t group_count,
     std::int64_t *group_sizes,
     T *scratchpad,
     std::int64_t scratchpad_size,
     const std::vector<cl::sycl::event> &events = {})
   }

Function supports the following precisions and devices.

.. list-table::
   :header-rows: 1

   * -  T
     -  Devices supported
   * -  ``float``
     -  Host, CPU, and GPU
   * -  ``double``
     -  Host, CPU, and GPU
   * -  ``std::complex<float>``
     -  Host, CPU, and GPU
   * -  ``std::complex<double>``
     -  Host, CPU, and GPU


Input Parameters
----------------

queue
   Device queue where calculations will be performed.

n
   Array of ``group_count`` parameters ``n``\ :sub:`g` specifying the
   order of the matrices ``A``\ :sub:`i` (0 ≤ ``n``\ :sub:`g`)
   belonging to group ``g``.

a
   Result of the :ref:`getrf_batch-group-version`
   function

lda
   Array of ``group_count`` parameters lda\ :sub:`g` specifying the
   leading dimension of ``A``\ :sub:`i` (``n``\ :sub:`g` ≤
   lda\ :sub:`g`) belonging to group ``g``.


ipiv
   The array as returned by :ref:`getrf_batch-group-version`.


group_count
   Specifies the number of groups of parameters. Must be at least 0.


group_sizes
   Array of group_count integers. Array element with index ``g``
   specifies the number of problems to solve for each of the groups
   of parameters ``g``. So the total number of problems to solve,
   ``batch_size``, is a sum of all parameter group sizes.


scratchpad
   Scratchpad memory to be used by routine for storing intermediate
   results.


scratchpad_size
   Size of scratchpad memory as a number of floating point elements
   of type T. Size should not be less then the value returned by
   :ref:`getri_batch_scratchpad_size-group-version`.


events
   List of events to wait for before starting computation. Defaults
   to empty list.


Output Parameters
-----------------


a
   Overwritten by the ``n``\ :sub:`g`-by-``n``\ :sub:`g` matrices
   ``A``\ :sub:`i`\ :sup:`-1`.


Exceptions
----------

.. tabularcolumns:: |\Y{0.3}|\Y{0.7}|

.. list-table::
   :header-rows: 1

   * - Exception
     - Description

   * -     ``mkl::lapack::batch_exception``
     -     This exception is thrown when problems occur during    calculations. You can obtain the info code of the problem using the   info() method of the exception object:

           If   ``info = -n``, the ``n``-th parameter had an illegal   value.

           If ``info`` equals the value passed as   scratchpad size, and detail() returns non-zero, then the passed   scratchpad is of insufficient size, and the required size should be   not less then value returned by the detail() method of the exception   object.


Return Values
-------------

Output event to wait on to ensure computation is complete.